Ongoing climate change is a major threat to biodiversity. As abiotic tolerances and dispersal abilities vary, species-specific responses have the potential to further amplify or ameliorate the ensuing impacts on species assemblages. Here, we investigate the effects of climate change on species distributions across non-marine birds, quantifying its projected impact on species richness (SR) as well as on different aspects of phylogenetic diversity globally. Going beyond previous work, we disentangle the potential impacts of species gains versus losses on assemblage-level phylogenetic diversity under climate change and compare the projected impacts to randomized assemblage changes. We show that beyond its effects on SR, climate change could have profound impacts on assemblage-level phylogenetic diversity and composition, which differ significantly from random changes and among regions. Though marked species losses are most frequent in tropical and subtropical areas in our projections, phylogenetic restructuring of species communities is likely to occur all across the globe. Furthermore, our results indicate that the most severe changes to the phylogenetic diversity of local assemblages are likely to be caused by species range shifts and local species gains rather than range reductions and extinctions. Our findings highlight the importance of considering diverse measures in climate impact assessments.